What is laplacetransform cos^2(14t) ?

The answer to laplacetransform cos^2(14t) is 1/(2s)+s/(2(s^2+784))

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laplacetransform cos^2(14t)

laplace transform

cos^{2} (14 t)

\frac{1}{2 s} + \frac{s}{2 ( s ^{2} + 784 )}

Solution steps

L {cos^{2} (14 t)}

Rewrite using trig identities

L {\frac{1}{2} + \frac{1}{2} cos (28 t)}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {\frac{1}{2}} + \frac{1}{2} L {cos (28 t)}

L {\frac{1}{2}} : \frac{1}{2 s}

L {cos (28 t)} : \frac{s}{s ^{2} + 784}

= \frac{1}{2 s} + \frac{1}{2} \cdot \frac{s}{s ^{2} + 784}

Refine

\frac{1}{2 s} + \frac{1}{2} \frac{s}{s ^{2} + 784} : \frac{1}{2 s} + \frac{s}{2 ( s ^{2} + 784 )}

= \frac{1}{2 s} + \frac{s}{2 ( s ^{2} + 784 )}

\frac{s - 1}{s ( s + 4 ) + 3}

y^{^{''}} + 2 y = 0

x \to \infty lim (10 + 3 x)

\frac{d}{d x} ((x - \frac{1}{x ^{2}})^{5})

\int \frac{11 + u}{u} d u

What is laplacetransform cos^2(14t) ?
The answer to laplacetransform cos^2(14t) is 1/(2s)+s/(2(s^2+784))